Question

You would like to test the null hypothesis H0 : µ = 2 against the alternative hypothesis H1 : µ > 2. You decide to use the α = 0.05 significance level. Suppose you know the population standard deviation is some σ0. You draw a sample from the population distribution, and calculate a sample mean of x = 2.2, with a corresponding p-value of p = 0.07. Assume all calculations have been done correctly. 1. If you repeat this experiment 100 times, in about how many of these samples do you expect to find the sample mean x >_ 2.2, assuming that the null hypothesis is true?A. 5 B. 7 C. 50 D. 93 E. 95

Answer 1

B. 7

Explanation:

H0 : µ = 2

H1 : µ > 2

sample mean is 2.2 with p-value=0.07

Since p-value>significance level (0.05) we fail to reject the null hypothesis. And p-value=0.07 means that the sample mean 2.2 is the border for highest 7.th percentile where sampling distribution is assumed as in the null hypothesis.

Thus, the probability of observing sample means higher than 2.2 is 0.07. If you repeat this experiment 100 times, you can expect 7 of these samples has mean >2.2.